Question

Suppose that q=40, L=5 and K=25 is a point on the production function

q=f(L,K).

Is it posssible for q=40, L=55, and K=26 to also be a point on this production function? Why or why not?

The combination q= 40, Lequals=5, and Kequals=26

A.can be a point because we assume production functions hold technology constant.

B.cannot be a point because we assume production functions represent the short run.

C.cannot be a point because we assume production functions are comprised of fixed inputs.

D.cannot be a point because we assume production functions are efficient.

E.can be a point because we assume production functions exhibit diminishing returns.

Answer #1

Since the output is also constant, it is more efficient to use less units of inputs into production. If the same output can be produced using less units of capital (K), then it is inefficient to use an extra unit as it will only add to the cost and not to the revenue.

Thus, adding another unit of capital (K) is not required and inefficient because earlier the same was being produced using a unit less than this input mix.

Therefore, the correct answer is option **d. cannot be a
point because we assume production functions are
efficient**.

1. Consider the following production function:
Y=F(A,L,K)=A(K^α)(L^(1-α))
where α < 1.
a. Derive the Marginal Product of Labor(MPL).
b. Show that this production function
exhibit diminishing MPL.
c. Derive the Marginal Production of Technology (MPA).
d. Does this production function exhibit diminishing MPA? Prove
or disprove

An electronics plant’s production function is Q = L 2K, where Q
is its output rate, L is the amount of labour it uses per period,
and K is the amount of capital it uses per period.
(a) Calculate the marginal product of labour (MPL) and the
marginal product of capital (MPK) for this production function.
Hint: MPK = dQ/dK. When taking the derivative with respect to K,
treat L as constant. For example when Q = L 3K2 ,...

Consider the production function Q = f(L,K) = 10KL / K+L. The
marginal products of labor and capital for this function are given
by
MPL = 10K^2 / (K +L)^2, MPK = 10L^2 / (K +L)^2.
(a) In the short run, assume that capital is fixed at K = 4.
What is the production function for the firm (quantity as a
function of labor only)? What are the average and marginal products
of labor? Draw APL and MPL on one...

5. Suppose a firm’s production function is Q = K.25L.25. The MPK
= .25K-.25L.25 and MPL = .25K.25L-.25. The price of K is 1 and the
price of L is 2.
• Derive the conditional demand functions for K and L
• Derive the long-run cost function

2. A firm has the following linear production function:
q = 5L + 2K
a. Does this firm’s production function exhibit diminishing
returns to labor?
b. Does this production function exhibit diminishing returns to
capital?
c. Graph the isoquant associated with q = 20.
d. What is the firm’s MRTS between K and L?
e. Does this production technology exhibit decreasing, constant,
or increasing returns to scale?

The production function for the Roundtree Laser Company is:
Q=(10L^.5)(K^.3)(M^.3)
where: Q: number of lasers produced per week L: amount of labor
used per week K: the amount of capital used per week M: quantity of
raw materials used per week
a) Does the production function exhibit decreasing returns to
scale?
b) Does the production function exhibit diminishing marginal
returns?

Suppose that the production function for Hannah and Sam’s home
remodeling business is
Q=F(L,K)Q=F(L,K)
Q=10L0.2K0.3.Q=10L0.2K0.3.
The wage rate is $1,500 per week and the cost of renting a unit of
capital is $1,000 per week. What is their cost function?
Instructions: Enter your answer as a whole
number.
C(Q) = Q2.

The firms production function is: Q=2L^2/3 K^1/3
A) Suppose the firm wants to determine the cost minimizing
combination for L and K for any given values of q, w, and r. Solve
for the the firms factor demand functions for L and K (i.e. express
the optimal quantity of L and K in terms of W, r and Q)
B) Using these factor demand functions, solve for the firm's
long run cost function.

Suppose that the production function for Hannah and Sam's home
remodeling business is
Q
= F(L,K)
Q
= 10L0.4K0.1.
Assume the wage rate is $8,000 per week and the cost of renting a
unit of capital is $2,000 per week.
a. What is the least-cost input combination for remodeling 400
square feet each week?
units of labor and units
of capital.
b. What is the total cost?
Instructions: Round your
answer to 2 decimal places.

Suppose one firm has production function f(K, L) =√K+√L, and
another firm has the production function f(K, L) = (√K+√L)^(.3).
Will these firms have the same supply functions?
Show your work

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